This is really fascinating. I remember seeing that little video of Barney singing with Dolly Parton a few times, same for Love to read with Barney, 1993.
The tea kettle Barney is holding in the live show looks very similar to the one that was used as the head for Michael’s robot costume in the episode The Queen of Make Believe.
These three puppets being in this book was before Drizzle the Dragon (Bard) was used in Baby Mozart the same goes for Boss Bird on Sesame Street and The Three Dino Puppets including the dragon also appeared in The Puzzle Place Episode called Spud Buds where they have different custom designs made by Clare Scholz and the team from Legends and Lore Company.
Well in the 1999 Barney and Baby Bop Go to the Libary Book there's three legends and Lore puppets that appeared in the puppet there which is Steggy Stegosaurus, Youri the Yourasaurus, and Pterry the Pterodactyl.